Problem: Simplify the following expression: $k = \dfrac{5hf + 5f}{5gf + 5f} + \dfrac{5f^2 + 30hf}{5gf + 5f}$ You can assume $f,g,h \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{5hf + 5f + 5f^2 + 30hf}{5gf + 5f}$ $k = \dfrac{35hf + 5f + 5f^2}{5gf + 5f}$ The numerator and denominator have a common factor of $5f$, so we can simplify $k = \dfrac{7h + 1 + f}{g + 1}$